Cohomologie de fibrés en droite sur le fibré cotangent de variétés grassmanniennes généralisées

Cette thèse s'intéresse à la cohomologie de fibrés en droite sur le fibré cotangent de variétés projectives. Plus précisément, pour $G$ un groupe algébrique simple, connexe et simplement connexe, $P$ un sous-groupe maximal de $G$ et $\omega$ un générateur dominant du groupe de caractères de $P$, on cherche à comprendre les groupes de cohomologie $H^i(T^*(G/P),\mathcal{L})$ où $\mathcal{L}$ est le faisceau des sections d'un fibré en droite sur $T^*(G/P)$. Sous certaines conditions, nous allons montrer qu'il existe un isomorphisme, à graduation près, entre $H^i(T^*(G/P),\mathcal{L})$ et $H^i(T^*(G/P),\mathcal{L}^{\vee})$ Après avoir travaillé dans un contexte théorique, nous nous intéresserons à certains sous-groupes paraboliques en lien avec les orbites nilpotentes. Dans ce cas, l'algèbre de Lie du radical unipotent de $P$, que nous noterons $\nLie$, a une structure d'espace vectoriel préhomogène. Nous pourrons alors déterminer quels cas vérifient les hypothèses nécessaires à la preuve de l'isomorphisme en montrant l'existence d'un $P$-covariant $f$ dans $\comp[\nLie]$ et en étudiant ses propriétés. Nous nous intéresserons ensuite aux singularités de la variété affine $V(f)$. Nous serons en mesure de montrer que sa normalisation est à singularités rationnelles.

Variétés de drapeaux et opérateurs différentiels

Soit G un groupe algébrique semi-simple sur un corps de caractéristique 0. Ce mémoire discute d'un théorème d'annulation de la cohomologie supérieure du faisceau D des opérateurs différentiels sur une variété de drapeaux de G. On démontre que si P est un sous-groupe parabolique de G, alors H^i(G/P,D)=0 pour tout i>0. On donne en fait trois preuves indépendantes de ce théorème. La première preuve est de Hesselink et n'est valide que dans le cas où le sous-groupe parabolique est un sous-groupe de Borel. Elle utilise un argument de suites spectrales et le théorème de Borel-Weil-Bott. La seconde preuve est de Kempf et n'est valide que dans le cas où le radical unipotent de P agit trivialement sur son algèbre de Lie. Elle n'utilise que le théorème de Borel-Weil-Bott. Enfin, la troisième preuve est attribuée à Elkik. Elle est valide pour tout sous-groupe parabolique mais utilise le théorème de Grauert-Riemenschneider. On présente aussi une construction détaillée du faisceau des opérateurs différentiels sur une variété.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Cost-effectiveness of a central venous catheter care bundle

Background: A bundled approach to central venous catheter care is currently being promoted as an effective way of preventing catheter-related bloodstream infection (CR-BSI). Consumables used in the bundled approach are relatively inexpensive which may lead to the conclusion that the bundle is cost-effective. However, this fails to consider the nontrivial costs of the monitoring and education activities required to implement the bundle, or that alternative strategies are available to prevent CR-BSI. We evaluated the cost-effectiveness of a bundle to prevent CR-BSI in Australian intensive care patients. ---------- Methods and Findings: A Markov decision model was used to evaluate the cost-effectiveness of the bundle relative to remaining with current practice (a non-bundled approach to catheter care and uncoated catheters), or use of antimicrobial catheters. We assumed the bundle reduced relative risk of CR-BSI to 0.34. Given uncertainty about the cost of the bundle, threshold analyses were used to determine the maximum cost at which the bundle remained cost-effective relative to the other approaches to infection control. Sensitivity analyses explored how this threshold alters under different assumptions about the economic value placed on bed-days and health benefits gained by preventing infection. If clinicians are prepared to use antimicrobial catheters, the bundle is cost-effective if national 18-month implementation costs are below $1.1 million. If antimicrobial catheters are not an option the bundle must cost less than $4.3 million. If decision makers are only interested in obtaining cash-savings for the unit, and place no economic value on either the bed-days or the health benefits gained through preventing infection, these cost thresholds are reduced by two-thirds.---------- Conclusions: A catheter care bundle has the potential to be cost-effective in the Australian intensive care setting. Rather than anticipating cash-savings from this intervention, decision makers must be prepared to invest resources in infection control to see efficiency improvements.

A robust structure and motion replacement for bundle adjustment

This paper demonstrates the application of a robust form of pose estimation and scene reconstruction using data from camera images. We demonstrate results that suggest the ability of the algorithm to rival methods of RANSAC based pose estimation polished by bundle adjustment in terms of solution robustness, speed and accuracy, even when given poor initialisations. Our simulated results show the behaviour of the algorithm in a number of novel simulated scenarios reflective of real world cases that show the ability of the algorithm to handle large observation noise and difficult reconstruction scenes. These results have a number of implications for the vision and robotics community, and show that the application of visual motion estimation on robotic platforms in an online fashion is approaching real-world feasibility.

Bi-objective bundle adjustment: towards large-scale visual sea-floor mapping with a minimal sensor suite

Visual sea-floor mapping is a rapidly growing application for Autonomous Underwater Vehicles (AUVs). AUVs are well-suited to the task as they remove humans from a potentially dangerous environment, can reach depths human divers cannot, and are capable of long-term operation in adverse conditions. The output of sea-floor maps generated by AUVs has a number of applications in scientific monitoring: from classifying coral in high biological value sites to surveying sea sponges to evaluate marine environment health.

Visual sea-floor mapping from low overlap imagery using bi-objective bundle adjustment and constrained motion

In most visual mapping applications suited to Autonomous Underwater Vehicles (AUVs), stereo visual odometry (VO) is rarely utilised as a pose estimator as imagery is typically of very low framerate due to energy conservation and data storage requirements. This adversely affects the robustness of a vision-based pose estimator and its ability to generate a smooth trajectory. This paper presents a novel VO pipeline for low-overlap imagery from an AUV that utilises constrained motion and integrates magnetometer data in a bi-objective bundle adjustment stage to achieve low-drift pose estimates over large trajectories. We analyse the performance of a standard stereo VO algorithm and compare the results to the modified vo algorithm. Results are demonstrated in a virtual environment in addition to low-overlap imagery gathered from an AUV. The modified VO algorithm shows significantly improved pose accuracy and performance over trajectories of more than 300m. In addition, dense 3D meshes generated from the visual odometry pipeline are presented as a qualitative output of the solution.

Integration-segregation decisions under general value functions: "create your own bundle - choose 1, 2, or all 3!",

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call ‘exposure units’ to naturally cover manifold scenarios spanning well beyond ‘products’. Our findings show, e.g. that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e. all are gains) or all negative (i.e. all are losses). In the case of exposure units with mixed-sign values, decision rules are much more complex and rely on cataloging the Bell number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper, we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

Resection-intersection bundle adjustment revisited

Bundle adjustment is one of the essential components of the computer vision toolbox. This paper revisits the resection-intersection approach, which has previously been shown to have inferior convergence properties. Modifications are proposed that greatly improve the performance of this method, resulting in a fast and accurate approach. Firstly, a linear triangulation step is added to the intersection stage, yielding higher accuracy and improved convergence rate. Secondly, the effect of parameter updates is tracked in order to reduce wasteful computation; only variables coupled to significantly changing variables are updated. This leads to significant improvements in computation time, at the cost of a small, controllable increase in error. Loop closures are handled effectively without the need for additional network modelling. The proposed approach is shown experimentally to yield comparable accuracy to a full sparse bundle adjustment (20% error increase) while computation time scales much better with the number of variables. Experiments on a progressive reconstruction system show the proposed method to be more efficient by a factor of 65 to 177, and 4.5 times more accurate (increasing over time) than a localised sparse bundle adjustment approach.

Particle size distribution effects on preferential deposition areas in metal foam wrapped tube bundle

This paper presents a numerical model for understanding particle transport and deposition in metal foam heat exchangers. Two-dimensional steady and unsteady numerical simulations of a standard single row metal foam-wrapped tube bundle are performed for different particle size distributions, i.e. uniform and normal distributions. Effects of different particle sizes and fluid inlet velocities on the overall particle transport inside and outside the foam layer are also investigated. It was noted that the simplification made in the previously-published numerical works in the literature, e.g. uniform particle deposition in the foam, is not necessarily accurate at least for the cases considered here. The results highlight the preferential particle deposition areas both along the tube walls and inside the foam using a developed particle deposition likelihood matrix. This likelihood matrix is developed based on three criteria being particle local velocity, time spent in the foam, and volume fraction. It was noted that the particles tend to deposit near both front and rear stagnation points. The former is explained by the higher momentum and direct exposure of the particles to the foam while the latter only accommodate small particles which can be entrained in the recirculation region formed behind the foam-wrapped tubes.

A two-arm cluster randomized control trial to determine the effectiveness of a pressure ulcer prevention bundle for critically ill patients

Purpose This study tested the effectiveness of a pressure ulcer (PU) prevention bundle in reducing the incidence of PUs in critically ill patients in two Saudi intensive care units (ICUs). Design A two-arm cluster randomized experimental control trial. Methods Participants in the intervention group received the PU prevention bundle, while the control group received standard skin care as per the local ICU policies. Data collected included demographic variables (age, diagnosis, comorbidities, admission trajectory, length of stay) and clinical variables (Braden Scale score, severity of organ function score, mechanical ventilation, PU presence, and staging). All patients were followed every two days from admission through to discharge, death, or up to a maximum of 28 days. Data were analyzed with descriptive correlation statistics, Kaplan-Meier survival analysis, and Poisson regression. Findings The total number of participants recruited was 140: 70 control participants (with a total of 728 days of observation) and 70 intervention participants (784 days of observation). PU cumulative incidence was significantly lower in the intervention group (7.14%) compared to the control group (32.86%). Poisson regression revealed the likelihood of PU development was 70% lower in the intervention group. The intervention group had significantly less Stage I (p = 002) and Stage II PU development (p = 026). Conclusions Significant improvements were observed in PU-related outcomes with the implementation of the PU prevention bundle in the ICU; PU incidence, severity, and total number of PUs per patient were reduced. Clinical Relevance Utilizing a bundle approach and standardized nursing language through skin assessment and translation of the knowledge to practice has the potential to impact positively on the quality of care and patient outcome.

Reducing pressure injuries in critically ill patients by using a patient skin integrity care bundle (InSPiRE)

Purpose To test an interventional patient skin integrity bundle, InSPiRE protocol, on the impact of pressure injuries (PrIs) in critically ill patients in an Australian adult intensive care unit (ICU). Methods Before and after design was used where the group of patients receiving the intervention (InSPiRE protocol) was compared with a similar control group who received standard care. Data collected included demographic and clinical variables, skin assessment, PrI presence and stage, and a Sequential Organ Failure Assessment (SOFA) score. Results Overall, 207 patients were enrolled, 105 in the intervention group and 102 in the control group. Most patients were men, mean age 55. The groups were similar on major demographic variables (age, SOFA scores, ICU length of stay). Pressure injury cumulative incidence was significantly lower in the intervention group (18%) compared to the control group for skin injuries(30.4%) (χ2=4.271, df=1, p=0.039) and mucous injuries (t test =3.27, p=<0.001) . Significantly fewer PrIs developing over time in the intervention group (Logrank= 11.842, df=1, p=<0.001) and patients developed fewer skin injuries (>3 PrIs/patient = 1/105) compared with the control group (>3 injuries/patient = 10/102) (p=0.018). Conclusion The intervention group, recieving the InSPiRE protocol, had lower PrI cumulative incidence, and reduced number and severity of PrIs that developed over time. Systematic and ongoing assessment of the patient's skin and PrI risk as well as implementation of tailored prevention measures are central to preventing PrIs.

Preventing infections through cleaner hospitals (PITCH): An environmental cleaning bundle

Translating the numerous lengthy cleaning standards and guidelines into meaningful and sustained improvements in cleaning practice is challenging. This research hypothesized that an evidence based cleaning bundle would improve cleaning performance, knowledge and attitudes, and ultimately reduces healthcare associated infections (HAI) in a way that is value for money. A bundle is a small, straightforward set of evidence based practices, that when performed collectively and reliably, improves patient outcomes.

Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation

A numerical study of conjugate natural convection and surface radiation in a horizontal hexagonal sheath housing 19 solid heat generating rods with cladding and argon as the fill gas, is performed. The natural convection in the sheath is driven by the volumetric heat generation in the solid rods. The problem is solved using the FLUENT CFD code. A correlation is obtained to predict the maximum temperature in the rod bundle for different pitch-to-diameter ratios and heat generating rates. The effective thermal conductivity is related to the heat generation rate, maximum temperature and the sheath temperature. Results are presented for the dimensionless maximum temperature, Rayleigh number and the contribution of radiation with changing emissivity, total wattage and the pitch-to-diameter ratio. In the simulation of a larger system that contains a rod bundle, the effective thermal conductivity facilitates simplified modelling of the rod bundle by treating it as a solid of effective thermal conductivity. The parametric studies revealed that the contribution of radiation can be 38-65% of the total heat generation, for the parameter ranges chosen. Data for critical Rayleigh number above which natural convection comes into effect is also presented. (C) 2011 Elsevier B.V. All rights reserved.